Method and apparatus of cross-correlation

ABSTRACT

Briefly, a method and apparatus to calculate cross-correlation values of complex binary sequences are provided. The apparatus may include a transformation unit and a cross-correlator. The cross-correlator may include a cross-correlation controller to provide, based on a type bit and a sign bit, a real component and/or an imaginary component of signals of complex binary sequences to a real accumulator and/or to an imaginary accumulator.

BACKGROUND OF THE INVENTION

In wireless communication systems such as spread spectrum cellularcommunication systems, cross-correlators may be used to perform crosscorrelation between streams of sequences of spread spectrum signals. Forexample, in cellular wideband code division multiple access (WCDMA)systems a spread spectrum signal may include a coding sequence, forexample, a pseudo-random code. In cellular wideband code divisionmultiple access (WCDMA) systems, the pseudo-random code may be anM-sequence or a Gold Sequence which has good “noise like” properties andis simple to construct. Furthermore, the sequences of the spreadspectrum signal may be the product of a 64 chip Walsh code (aimed atseparating up to 64 different users per base) and a periodicpseudorandom noise (PN) sequence (aimed at separating the differentbases).

Cross-correlators may be used to perform cross-correlation between thestreams of sequences. However, existing hardware implementations ofcross-correlators may include a large number of components and mayconsume large currents.

Thus, there is a need for hardware and/or software implementations forcalculating cross-correlation values to mitigate the above-describeddisadvantages.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter regarded as the invention is particularly pointed outand distinctly claimed in the concluding portion of the specification.The invention, however, both as to organization and method of operation,together with objects, features and advantages thereof, may best beunderstood by reference to the following detailed description when readwith the accompanied drawings in which:

FIG. 1 is a schematic flowchart depicting a method according to anexemplary embodiment of the present invention;

FIG. 2 is a schematic illustration helpful in understanding a phaserotation according to some exemplary embodiments of the presentinvention; and

FIG. 3 is a schematic diagram of a receiver according to some exemplaryembodiments of the present invention.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However it will be understood by those of ordinary skill in the art thatthe present invention may be practiced without these specific details.In other instances, well-known methods, procedures, components andcircuits have not been described in detail so as not to obscure thepresent invention.

Some portions of the detailed description which follow are presented interms of algorithms and symbolic representations of operations on databits or binary digital signals within a computer memory. Thesealgorithmic descriptions and representations may be the techniques usedby those skilled in the data processing arts to convey the substance oftheir work to others skilled in the art.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “processing,” “computing,”“calculating,” “determining,” or the like, refer to the action and/orprocesses of a computer or computing system, or similar electroniccomputing device, that manipulate and/or transform data represented asphysical, such as electronic, quantities within the computing system'sregisters and/or memories into other data similarly represented asphysical quantities within the computing system's memories, registers orother such information storage, transmission or display devices.

It should be understood that the present invention may be used invariety of applications. Although the present invention is not limitedin this respect, the circuits and techniques disclosed herein may beused in many apparatuses such as receivers of a radio system. Receiversintended to be included within the scope of the present inventioninclude, by a way of example only, cellular radiotelephone receivers,spread spectrum receivers, digital system receivers and a like.

Types of cellular radiotelephone receivers intended to be within thescope of the present invention include, although not limited to, CodeDivision Multiple Access (CDMA), CDMA 2000 and wideband CDMA (WCDMA)cellular radiotelephone, receivers for receiving spread spectrumsignals, and the like.

Turning to FIG. 1, a method of cross-correlating between at least twosignals of complex binary sequences according to an embodiment of theinvention is shown. Although the scope of the present invention is notlimited in this respect, the method may begin with transformingquadrature phase shift keying (QPSK) sequences into two signals ofcomplex binary sequences (block 100), if desired.

Although the scope of the present invention is not limited in thisrespect, the transforming of QPSK sequences into two signals of complexbinary sequences may be demonstrated by the following equations. Thefollowing equation may be used to calculate a complex cross correlationbetween two QPSK complex sequences: $\begin{matrix}{{{CC}\left( {n,d} \right)} = {\sum\limits_{i = 0}^{L - 1}{{S_{1}\left( {n + {\mathbb{i}}} \right)} \cdot {S_{2}^{*}\left( {n + {\mathbb{i}} + d} \right)}}}} & {{Equation}\quad 1}\end{matrix}$wherein:

S₁(n), S₂(n) are two signals of complex sequences with given complexvalues of ±A±j·A;

L is the number of cross correlation terms; and

d is the delay between the two sequences.Equation 1 may be further developed in the following manner:$\begin{matrix}\begin{matrix}{{{CC}\left( {n,d} \right)} = {\sum\limits_{i = 0}^{L - 1}{{S_{1}\left( {n + {\mathbb{i}}} \right)} \cdot {S_{2}^{*}\left( {n + {\mathbb{i}} + d} \right)}}}} \\{= {2 \cdot {\sum\limits_{i = 0}^{L - 1}{{{\overset{\sim}{S}}_{1}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2}^{*}\left( {n + {\mathbb{i}} + d} \right)}}}}}\end{matrix} & {{Equation}\quad 2}\end{matrix}$As demonstrated by Equation 2, the cross correlation sequences S₁(n),S₂(n) may be replaced by two signals of complex binary sequences {tildeover (S)}₁(n), {tilde over (S)}₂(n). The content of the signals {tildeover (S)}₁(n), {tilde over (S)}₂(n) may be depicted by the followingequation:{tilde over (S)} _(1I)(n)=(S _(1I)(n)+S _(1Q)(n))/2{tilde over (S)} _(1Q)(n)=(−S _(1I)(n)+S _(1Q)(n))/2{tilde over (S)} _(2I)(n)=(S _(2I)(n)+S _(2Q)(n))/2{tilde over (S)} _(2Q)(n)=(−S _(2I)(n)+S _(2Q)(n))/2  Equation 3wherein notation I may denote an in-phase component of signals {tildeover (S)}₁(n), {tilde over (S)}₂(n) and notation Q may denote aquadrature phase component of signals {tilde over (S)}₁(n), {tilde over(S)}₂(n). Furthermore, it should be known to one skilled in the art thatnotation I may represent a real component of signals {tilde over(S)}₁(n), {tilde over (S)}₂(n), and notation Q may represent animaginary component of signals {tilde over (S)}₁(n), {tilde over(S)}₂(n) signals.

Although the scope of the present invention is not limited in thisrespect, transformation of QPSK sequences to complex binary sequencesmay be performed by ±(π/4) phase rotation of QPSK sequences, asdescribed below with reference to FIG. 2.

Turning to FIG. 2, an illustration helpful for describing rotation ofQPSK sequences according to embodiments of the present invention isshown. Although the scope of the present invention is not limited inthis respect, FIG. 2 shows ±(π/4) rotations of QPSK sequence values.However, in other embodiment of the present invention, ±(π/4) rotationof 16 quadrature amplitude modulation (QAM) sequences or other suitableforms of sequence rotation may be performed, if desired. Morepractically, QPSK values X1, X2, X3, and X4 may be rotated to be oneither an imaginary axis or a real axis. For example, X1 may be rotatedto be on the real axis, X2 may be rotated to be on the imaginary axis,X3 may be rotated to be on the real axis and X4 may be rotated to be onthe imaginary axis. It should be understood to one skilled in the artthat rotating of QPSK sequence values may be analogues to transformingof QPSK sequences to real or imaginary components of a complex binarysequence, if desired.

Furthermore, the rotation may be utilized to simplify the crosscorrelation calculations, as described by the following equation:$\begin{matrix}{{{{\overset{\sim}{S}}_{1}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2}^{*}\left( {n + {\mathbb{i}} + d} \right)}} = \left\{ \begin{matrix}{{{\overset{\sim}{S}}_{1I}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2I}\left( {n + {\mathbb{i}} + d} \right)}} & {{{S_{1I}\left( {n + {\mathbb{i}}} \right)} = {S_{1Q}\left( {n + {\mathbb{i}}} \right)}},} \\\quad & {{S_{2I}\left( {n + {\mathbb{i}} + d} \right)} = {S_{2Q}\left( {n + {\mathbb{i}} + d} \right)}} \\{{- j} \cdot {{\overset{\sim}{S}}_{1I}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2Q}\left( {n + {\mathbb{i}} + d} \right)}} & {{{S_{1I}\left( {n + {\mathbb{i}}} \right)} = {S_{1Q}\left( {n + {\mathbb{i}}} \right)}},} \\\quad & {{S_{2I}\left( {n + {\mathbb{i}} + d} \right)} \neq {S_{2Q}\left( {n + {\mathbb{i}} + d} \right)}} \\{j \cdot {{\overset{\sim}{S}}_{1Q}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2I}\left( {n + {\mathbb{i}} + d} \right)}} & {{{S_{1I}\left( {n + {\mathbb{i}}} \right)} \neq {S_{1Q}\left( {n + {\mathbb{i}}} \right)}},} \\\quad & {{S_{2I}\left( {n + {\mathbb{i}} + d} \right)} = {S_{2Q}\left( {n + {\mathbb{i}} + d} \right)}} \\{{{\overset{\sim}{S}}_{1Q}\left( {n + {\mathbb{i}}} \right)} \cdot {{\overset{\sim}{S}}_{2Q}\left( {n + {\mathbb{i}} + d} \right)}} & {{{S_{1I}\left( {n + {\mathbb{i}}} \right)} \neq {S_{1Q}\left( {n + {\mathbb{i}}} \right)}},} \\\quad & {{S_{2I}\left( {n + {\mathbb{i}} + d} \right)} \neq {S_{2Q}\left( {n + {\mathbb{i}} + d} \right)}}\end{matrix} \right.} & {{Equation}\quad 4}\end{matrix}$As may be seen in Equation 4, the complex binary sequence signals {tildeover (S)}₁(n), {tilde over (S)}₂(n) are either purely real or purelyimaginary, which may reduce the number of real and/or imaginarymultiplications required for performing complex multiplication from fourto one.

Turning back to FIG. 1, the method may continue with transforming acomplex sequence into a sign bit and a type bit representation (block110). For example, as shown in FIG. 2, a rotation and transformation ofthe value X1 may generate a sign bit “plus” and a type bit “real”.Furthermore, a rotation and transformation of the sequence X4 maygenerate a sign bit “minus” and a type bit “imaginary”. Although thepresent invention is not limited in this respect, rotation andtransformation of sequences may be performed in single operation, ifdesired. However, in other embodiments of the invention rotation andtransformation may be performed by separate operations. In addition, inone embodiment of the present invention, the type bit and the sign bitmay be used to provide a real component and/or an imaginary component ofthe complex binary sequences to real and/or imaginary accumulator,respectively (block 120).

Although the scope of the present invention is not limited in thisrespect, at least two accumulators may be used, a first accumulator maybe used to output a real component of cross-correlation results and thesecond accumulator may be used to output an imaginary component ofcross-correlation results.

The cross-correlation results may be multiplied by two, as demonstratedby Equation 2 (block 130). It should be understood by one skilled in theart that the above described method may be implemented by hardwareand/or by software. An example of an embodiment of the present inventionthat may use a combination of hardware and software will now bedescribed.

Turning to FIG. 3, a block diagram of a receiver 300 according to anembodiment of the present invention is shown. Although, the scope of thepresent invention is not limited in this respect, receiver 300 mayinclude an antenna 310, a transformation unit 315 that may includetransformers 320, 330, and a cross-correlator 400. Cross-correlator 400may include a cross-correlation controller 340, an accumulation unit 345that may include a real accumulator 350 and an imaginary accumulator 360and amplifiers 370, 380.

Although the scope of the present invention is not limited to thisexample, for simplicity of description, receiver 300 will be describedas a WCDMA receiver. Antenna 310 may receive signals, for example, pilotsignal, dedicated channel signal, or the like, that may include QPSKsequences. In some embodiments of the present invention antenna 310 maybe a dipole antenna, if desired. However, other types of antennas may beused.

A demodulator (not shown) may output two signals, S1(N) and S2*(N+D), ofQPSK sequences. Transformers 320 and 330 may receive signals S1(N) andS2*(N+D) of the QPSK sequences and may transform the QPSK sequences intotwo signals of complex binary sequences {tilde over (S)}₁(n) and {tildeover (S)}₂*(n), respectively. The transformation of QPSK sequences tocomplex binary sequences may be performed by ±(π/4) phase rotation ofthe QPSK sequences, as described in detail with reference to FIG. 2above. Furthermore, transformers 320 and 330 may provide control bitssuch as, for example, sign bits 325 and 335 and type bits 327 and 337,to cross-correlation controller 340.

Although the scope of the present invention is not limited in thisrespect, cross-correlation controller 340 may provide complex binarysequences via ports 341, 346 and may enable or disable accumulators 350,370 with ports 342, 347, respectively. More particularly,cross-correlation controller 340 may selectively control whichaccumulator may be active, using enable signals via ports 342, 347,according to sign bits 325, 335 and type bits 327, 337. An example ofsuch a selective control is described with reference to Table 1 below.

Although the scope of the present invention is not limited in thisrespect, in some embodiments of the present invention, a representationas shown in Table 1 below may be stored in a memory (not shown). Inaddition, in other embodiments of the present invention, arepresentation as shown in Table 1 below may be implemented by hardwareand/or by software. TABLE 1 Real Image Accumulator Accumulator Sign SignType Type (350) (360) Bit Bit Bit Bit En- En- Index (325) (335) (327)(337) Input able Input able 0 Plus Plus Real Real A On — Off 1 Plus PlusReal Image — Off A On 2 Plus Plus Image Real — Off A On 3 Plus PlusImage Image −A On — Off 4 Plus Minus Real Real −A On — Off 5 Plus MinusReal Image — Off −A On 6 Plus Minus Image Real — Off −A On 7 Plus MinusImage Image A On — Off 8 Minus Plus Real Real −A On — Off 9 Minus PlusReal Image — Off −A On 10 Minus Plus Image Real — Off −A On 11 MinusPlus Image Image A On — Off 12 Minus Minus Real Real A On — Off 13 MinusMinus Real Image — Off A On 14 Minus Minus Image Real — Off A On 15Minus Minus Image Image −A On — OffIn Table 1 the following notation used:“Index” represents indices of the complex binary sequence;“Sign Bits” (325, 335) represent the sign of the transformed sequence;“Type Bits” (335, 337) represent weather the transformed bit of thecomplex binary sequence is “Real” or “Image” (i.e., imaginary);“Input” represent which binary sequence may be provided to which of theaccumulators; and“Enable” represents whether or not the accumulator is enabled by theenable bit.

Although the scope of the present invention is not limited in thisrespect, cross-correlation controller 340 may select the complex binarysequences according to Table 1. The selected sequences may be inputtedto the selected accumulators 350 and/or 360, to be accumulated. Realaccumulator 350 and imaginary accumulator 360 may produce the totalReal/Image cross correlation results, respectively.

In addition, accumulators 350 and 360 may include an up/down counter andan AND gate (not shown). The AND gate may enable the up/down counteroperation. However, it should be understood that other accumulatorimplementations may be used. Although, the scope of the presentinvention is not limited in this respect, multipliers 370, 380 maymultiply the results of cross-correlation preformed by cross-correlationcontroller 340, real accumulator 350 and imaginary accumulator 360 bytwo, as depicted by Equation 2.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

1-24. (canceled)
 25. An apparatus comprising: a transformation unit totransform phase shift keying (PSK) sequences of first and second inputsignals into first and second signals of complex sequences; and across-correlator to cross-correlate the first and second signals ofcomplex sequences based on at least one bit provided by thetransformation unit, the cross-correlator including an accumulation unitto provide a real cross-correlated signal and an imaginarycross-correlated signal, and a cross-correlation controller to provide areal component of the first and second signals of complex sequences andan imaginary component of the first and second signals of complexsequences to the accumulation unit.
 26. The apparatus of claim 25,wherein the transformation unit comprises: a first transformer to rotatea phase of PSK sequences of the first input signal to provide theinformation of the first signal of complex sequences that include realand imaginary components; and a second transformer to rotate a phase ofPSK sequences of the second input signal to provide the information ofthe second signal of complex sequences that include real and imaginarycomponents.
 27. The apparatus of claim 25, wherein the PSK sequences arequardrature phase shift keying (QPSK) sequences.
 28. The apparatus ofclaim 25, wherein the complex sequences are complex binary sequences.29. The apparatus of claim 25, wherein the at least one bit provided bythe transformation unit comprises at least one of a sign bit or a typebit.
 30. The apparatus of claim 25, wherein the accumulation unitcomprises a first accumulator to provide the real cross-correlatedsignal and a second accumulator to provide the imaginarycross-correlated signal.
 31. The apparatus of claim 25, wherein thecross-correlator further comprises: a first multiplier to multiply thereal cross-correlated signal; and a second multiplier to multiply theimaginary cross-correlated signal.
 32. The apparatus of claim 31 whereinthe first and second multipliers are able to multiply the real andimaginary cross-correlated signals by two.
 33. The apparatus of claim26, wherein the first and second transformers are able to provide aphase rotation of ±(π/4) to bits of the first and second signals ofcomplex sequences.
 34. The apparatus of claim 26, wherein the first andsecond signals of complex sequences comprise values of ±A and ±j·A. 35.A method comprising: cross-correlating between a first signal of complexsequences and a second signal of complex sequences according to at leastone bit provided by phase-rotating the complex sequences of the firstand second signals; and transforming first and second input signals ofphase shift keying (PSK) sequences into the first and second signals ofcomplex sequences, wherein transforming includes rotating a phase of thePSK sequences of the first input signal and a phase of the PSK sequencesof the second input signal, and providing real and imaginary componentsof complex sequences of the first and second signals to an accumulationunit.
 36. The method of claim 35, wherein the PSK sequences arequardrature phase shift keying (QPSK) sequences.
 37. The method of claim35, wherein the complex sequences are complex binary sequences.
 38. Themethod of claim 35, wherein the at least one bit provided byphase-rotating comprises at least one of a sign bit or a type bit. 39.The method of claim 35, wherein the accumulation unit comprises a realaccumulator to which real components of complex sequences are providedand an imaginary accumulator to which imaginary components of complexsequences are provided.
 40. The method of claim 35, wherein thecross-correlating comprises multiplying results of the cross-correlatingby two.
 41. The method of claim 35, wherein rotating comprises rotatinga phase of the complex sequences by ±(π/4).
 42. An article comprising astorage medium having stored thereon instructions that when executedresult in: cross-correlating between a first signal of complex sequencesand a second signal of complex sequences according to at least one bitprovided by phase-rotating the complex sequences of the first and secondsignals; and transforming first and second input signals of phase shiftkeying (PSK) sequences into the first and second signals of complexsequences, wherein the instruction of transforming when executed furtherresults in: rotating a phase the PSK sequences of the first input signaland a phase of the PSK sequences of the second input signal, andproviding real and imaginary components of complex sequences of thefirst and second signals to an accumulation unit.
 43. The article ofclaim 42, wherein the PSK sequences are quardrature phase shift keying(QPSK) sequences.
 44. The article of claim 42, wherein the complexsequences are complex binary sequences.
 45. The article of claim 42,wherein the at least one bit provided by phase-rotating comprises atleast one of a sign bit or a type bit.
 46. The article of claim 42,wherein the accumulation unit comprises a real accumulator to which realcomponents of complex sequences are provided and an imaginaryaccumulator to which imaginary components of complex sequences areprovided.
 47. The article of claim 42, wherein the instructions whenexecuted further result in: cross-correlating between the complexsequences of the first and second signals and multiplying the results ofthe cross-correlating by two.
 48. The article of claim 42, wherein thephase of bits of the complex sequences are rotated by ±(π/4).